Artin formalism for Selberg zeta functions of co-finite Kleinian groups
Eliot Brenner[1]; Florin Spinu[2]
- [1] University of Minnesota 206 Church Street SE Minneapolis USA, 55455
- [2] Johns Hopkins University Baltimore USA, 21218
Journal de Théorie des Nombres de Bordeaux (2009)
- Volume: 21, Issue: 1, page 59-75
- ISSN: 1246-7405
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top- E. Brenner, F. Spinu, Artin Formalism, for Kleinian Groups, via Heat Kernel Methods. Submitted to Serge Lang Memorial Volume. Zbl1233.11057
- P. Cohen, P. Sarnak, Lecture notes on Selberg trace formula (unpublished).
- J. Elstrodt, F. Grunewald, J. Mennicke, Groups acting on hyperbolic space. Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998. Zbl0888.11001MR1483315
- J. Friedman, The Selberg trace formula and Selberg-zeta function for cofinite Kleinian groups with finite-dimensional unitary representations. Math. Zeit. 50 (2005), No.4. Zbl1135.11026MR2180383
- J. Friedman, Analogues of the Artin factorization formula for the automorphic scattering matrix and Selberg zeta-function associated to a Kleinian group. Arxiv:math/0702030. MR2415021
- R. Gangolli, G. Warner, Zeta functions of Selberg’s type for some noncompact quotients of symmetric spaces of rank one. Nagoya Math. J. 78 (1980), 1–44. MR571435
- J. Jorgenson, S. Lang, Artin formalism and heat kernels. Jour. Reine. Angew. Math. 447 (1994), 165–280. Zbl0789.11055MR1263173
- A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric spaces with applications to Dirichlet series. J. Indian Math. Soc. 20 (1956), 47–87. Zbl0072.08201MR88511
- A.B. Venkov, The Artin Takagi formula for Selberg’s zeta-function and the Roelcke conjecture. Soviet Math. Dokl. 20 (1979), No.4, 745–748. Zbl0432.30036
- A. B. Venkov, Spectral Theory of Automorphic Functions. Proceedings of the Steklov Institute of Mathematics 4, 1982. Zbl0501.10029MR692019
- A. B. Venkov, P. Zograf, Analogues of Artin’s factorization in the spectral theory of automorphic functions. Math. USSR Izvestiya 2 (1983), No. 3, 435–443. Zbl0527.10020